Hi

Standard Form of an Equation of an Hyperbola opening right and  left is:

   with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis

Foci are  units right and left of center along y = k

25x2+50x-9y2-18y-209=0   || putting into Standard form

 25(x+1)^2 - 9(y+1)^2 - 25 + 9 - 209 = 0

 25(x+1)^2 - 9(y+1)^2 = 225



center:  C(-1,1)

foci:  F(-1+,1)  and F(-1-,1) 

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